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Alexander Dodge’s glitzy set for the Old Globe’s Sammy includes stately, showcase-windowlike structures framed by rows of blinking lights. They feature props for the scene, or people who pose, in Fabio Toblini’s classy period costumes, and sometimes sing. The polished black structures roll on and off. It doesn’t take long to see that the musical, based on the life of Sammy Davis Jr., resembles the showcases. The life of an amazing entertainer rolls by, but from afar and at top speed. Watching Sammy feels like window-shopping from a passing car.

“Your whole life just moves too fast,” his wife May Britt tells Davis. The musical follows suit, with no time for development. Leslie Bricusse’s book creates such a shallow, itemized portrait that Davis remains a one-note character: he’s an orphan, a four-year-old wunderkind, has a car crash (loses an eye and his sense of balance; his struggle to overcome both, if told in detail, could have revealed more about the man); he marries, has affairs, does drugs, hugs Nixon, isn’t chasing his lost mother after all, earns Kennedy Center Award, finale, and curtain.

Name performers usually have a signature song. Davis had a handful, most of them written by Bricusse, often with Anthony Newley: “Once in a Lifetime,” “Who Can I Turn To?” “The Candy Man,” “What Kind of Fool Am I?” Davis could sell a song like few others. When Obba Babatundé sings them, however, he’s been encouraged to over-sell music that needs no extra hype.

The iconic numbers also create a problem. They dwarf those written specifically for the show. New songs — the ones sung to Davis, in particular (“Slow Down Sammy,” “Black Sammy, White Sammy”) — feel flat, and often preachy, by comparison.

Some portrayals verge on cartoon (Dean Martin, Sinatra, Eddie Cantor), and the women never rise above generic (an exception: Ann Duquesnay, outstanding as Davis’s grandmother Rose). Babatundé’s Davis has the hunched shoulders, the bebop head-nod, the firm grin, and manic energy down. And he sings and dances (and plays drums, for that matter) with bountiful gifts. Babatundé entertains throughout and deserves the jump-to-your-feet standing ovation the audience gives him. But in his nearly three-hour performance, Babatundé is, at best, only like Sammy Davis Jr. The hit-and-run script — scenes often just setups for the next song — never gives him the time to be the great entertainer.

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In Bryony Lavery’s Frozen, a researcher asks Ralph if he feels any remorse for raping and murdering seven young girls. Dead-faced Ralph says no. He’s just sorry “it’s not legal.”

Lavery based her play on the findings of psychiatrist Dorothy Otnow Lewis. In Guilty by Reason of Insanity, Lewis contends that profound abuse in childhood damages the brain’s cerebral cortex and hippocampus. One result: an inability to determine right from wrong. Thus the root causes of crime, she says, are neurological. They make serial killers “ill, not evil.” Lewis doesn’t absolve murderers — she advocates lifetime imprisonment without parole — but says they deserve our forgiveness.

“I think you’re lucky if forgiveness visits you,” the playwright said in an interview, “and you’re in agony if it doesn’t.” Lavery makes Frozen, and an ability to forgive Ralph, her test case.

Each of the play’s three characters is frozen: remorseless Ralph, Agnetha (a forensic psychologist, loosely based on Dorothy Lewis, in denial about a recent loss), and Nancy (whose ten-year-old daughter Ralph raped and suffocated). You could almost say the murder literally damaged Nancy’s left brain. Good and evil blur, and she’s never felt less alive. Her other daughter’s bromides about forgiving and “letting go” ring hollow.

In Ion Theatre’s stark, deeply moving production, Matt Scott gives Ralph the cold logic of an irrational mind. His thoughts would make sense in a parallel universe of cruelty. As the years pass, Agnetha and a visit by Nancy create an aperture back to a moral view. In one of his best efforts ever, Scott thaws from fierce to fragile, and Ralph’s re-entry shock becomes his undoing.

Director Claudio Raygoza has staged the piece on the perimeter. Scenes unfold on small stages and surround the audience with pain. The languid pacing of scenes, however, includes gaps and pauses more empty than pregnant. Sunny Smith, emotionally apt as Agnetha, would improve if she quickened her words, as would the production in general.

They say serial killers have 100 times more rage than “normal” people (whoever they are). Nancy Shirley begs to differ. In Dana Hooley’s excellent portrayal, the slaying of her daughter jumped Nancy into the cycle of violence. Her blast-furnace seething compares with Ralph’s, and Hooley more than suggests that, if given the chance, Nancy wouldn’t just murder Ralph; she’d relish it. How Hooley moves from blackout retribution to the open-eyed Nancy at the end is one compelling reason, among many, to see Frozen, which must close this weekend.